High‐order difference schemes for convection‐diffusion interface problems

Abstract

On non‐uniform mesh new high‐order compact finite difference approximations of the solution and the flux to convection‐diffusion interface problems in one‐dimension are constructed and analyzed. Explicit formulas based on new Marchuk integral identities that give O(h2), O(h4), . . . accuracy are derived. New numerical integration quadrature procedures for computing three‐point schemes of any prescribed order of accuracy are developed. Numerical experiments confirm the theoretical results. Straipsnyje sukonstruotos ir analizuojamos naujos aukštos eiles kompaktines baigtiniu skirtumu schemos, aproksimuojančios konvekcijos‐difuzijos saveikos uždavinius vienmačiu atveju. Gautos išreikštines O(h 2), O(h4), … eiles tikslumo formules, pagristos Marchuko integralinemis tapatybemis. Išvestos naujos skaitmeninio integravimo kvadratūrines nurodyto tikslumo formules tritaškiu schemu skaičiavimui. Pateikti skaitiniai eksperimentai, patvirtinantys teorinius rezultatus. First Published Online: 14 Oct 2010

Keywords

• high‐order difference schemes
• convection‐diffusion interface problems
• numerical integration quadrature